We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of...

We use a panel survey of ~19,000 primary-school-aged children in rural Tamil Nadu to study 'learning loss' after COVID-19-induced school closures, and the pace of recovery after schools reopened. Students tested in December 2021 (18 months after school closures) displayed learning deficits of...

This paper develops linear estimators for structural and causal parameters in nonparametric,nonseparable models using panel data. These models incorporate unobserved, time-varying, individual heterogeneity, which may be correlated with the regressors. Estimation is based on an approximation of...

In this paper, we provide a suite of tools for empirical market design, including optimal nonlinear pricing in intensive-margin consumer demand, as well as a broad class of related adverse-selection models. Despite significant data limitations, we are able to derive informative bounds on demand...

Given the ubiquitous presence of endogenous regressors and the challenges in finding good instruments to overcome the endogeneity problem, a forefront of recent research is the development and application of endogeneity correction methods without requiring instruments. In this article, we...

This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in...

We study the interpretation of regressions with multiple treatments and flexible controls. Such regressions are often used to analyze stratified randomized control trials with multiple intervention arms, to estimate value-added (for, e.g., teachers) with observational data, and to leverage the...

Researchers increasingly have access to two types of data: (i) large observational datasets where treatment (e.g., class size) is not randomized but several primary outcomes (e.g., graduation rates) and secondary outcomes (e.g., test scores) are observed and (ii) experimental data in which...